In a medium saucepan, cover asparagus with cold water. Bring to boiling; boil for 1 minute. Remove from heat; drain and plunge asparagus into ice water. Drain.
In a bowl, combine asparagus, crabmeat, and celery. Line each of 4 salad plates with 2 to 3 romaine leaves or some of the torn mixed greens. Divide asparagus mixture among plates.
For dressing, in a screw-top jar, combine oil, lemon juice, vinegar, onion, mustard, parsley, chives, dill, pepper, and salt. Cover and shake until well combined. Drizzle over salad mixture. Garnish with lemon wedges. Makes 4 servings.
To prepare the asparagus, wash and scrape off the scales, if you like. Break off the woody bases. If using canned crabmeat, omit the salt in the dressing.